Expression and interpretation of negation: a bidirectional OT typology

Henriëtte de Swart

Utrecht University

Expressing negation

Natural languages: ways to express negation/denial: not.

First-order propositional connective Natural languages: negative indefinites, nobody.

First-order quantifier x.

Negation and cognition

Assumption: something like or something equivalent to first-order logic part of general human cognition.

Prediction: negation and negative quantifiers behave alike across languages.

Prediction falsified by data.

Quanta Costa?

DN and NC

Nobody said nothing. (Eng) xy

Niemand zei niets. (Dutch) xy

Nadie miraba a nadie. (Spa) xy

Nessuno ha parlato con nessuno. (Ital) xy

Personne n’a rien dit. (Fr)ambiguous

Negation in context

Double negation versus negative concord

negative quantifiers versus n-words.

In isolation: same form, same meaning.

In a sequence: same forms, different meanings.

De Swart & Sag (2002)

Lexical claim: n-words denote negative quantifiers, just like negative indefinites.Syntax-semantics interface (HPSG): N-store collects all negative quantifiers; interpretation upon retrieval.Semantic claim: polyadic quantification. Iteration double negation. Resumption negative concord.

Main insights

Polyadic quantification/HPSG grammar: defines space of possible meanings in language.No lexical difference between negative quantifiers and n-words. No ‘hidden’ negations in syntax.Retrieval determines meaning at the syntax-semantics interface.

Grammar and typology

Grammar does not predict when iteration or resumption arises.

Cross-linguistic variation: typology.

Two main classes: negative concord languages (NC) and double negation languages (DN).

Modeling typology?

Richter and Sailer (2006): complement general rules of grammar with language specific constraints.

NC languages: Negation Complexity constraint (Romance, Slavic..).

DN languages: Negation Faithfulness constraint (English, German, ..).

Evaluation

Why do languages ‘bother’ to develop these additional constraints?

Relation between constraints? Typological theory?

How to account for language change in the system of negation?

Typology in OT

All constraints are universal.

Constraints are soft (violable).

Ranking of constraints determined by language-specific grammar.

Typology by reranking.

Diachronic change: (gradual) process of promotion/demotion of constraints.

Syntax-semantics interface

OT syntax: choose the optimal form for a given meaning.

OT semantics: choose the optimal interpretation for a given form.

Bi-directional OT: evaluate pairs of form and meaning.

Propositional negation

Production issue: how does a language express the meaning p?

FaithNeg: reflect non-affirmativity of the input in the output.

Faithfulness constraint

‘double-edged’ constraint: both in OT syntax, and in OT semantics.

Markedness of negation

*Neg: avoid negation in the output.

Markedness constraint

FaithNeg >> *Neg

Ranking fixed across languages

Negation is marked in form/meaning (opposed to affirmation).

Propositional negation

Meaning

form FaithNeg *Neg

It is raining *

It is not raining *

Negative sentences

It is not raining. [English]

No vino Pedro. [Spanish] Not came Pedro.

Ni fydd Sioned yna. [Welsh]

Not be.fut Sioned there.

Interpretation

F\form It is not raining

meaning FaithNeg *Neg

*

*

Bi-directional optimization

f: it is raining

f’: it is not raining

m: m’:

FNeg *Neg

<raining, >

<raining, > * *

<not raining, > * *

<not raining, > **

Indefinites under negation

Production: how do languages express the meaning x1 x2 x3 P(x1, x2, x3)?

Three cases: o plain indefinites, o negative polarity items, o n-words.

indefinites

Example: Dutch, Turkish, ..

Ik heb niet onmiddellijk iets gekocht.

I have not immediately something bought.

Niemand heeft iets aan iemand gezegd.

No one has something to someone said.

Negative polarity items

Languages in which plain indefinites are positive polarity items may use negative polarity items.

Example: English, Basque, ..

*I did not buy something

I did not buy anything.

Nobody said anything to anyone.

N-words

Languages in which plain indefinites are positive polarity items may use n-words.

N-words denote x in isolation, but express a single negative statement together with sentential negation or other n-words (x1 x2 x3).

Example: Spanish

A: Qué viste? B: Nada

A: What did you see? B: nothing.

No vino nadie.

Not came nobody.

Nadie miraba a nadie

Nobody looked at nobody.

NPIs and n-words

N-words denote x in isolation, NPIs (n particular minimizers) denote x.NPIs have to be licensed, n-words are ‘self-licensing’ (preverbal, fragment answers).Negative concord is limited to anti-additive contexts, many NPIs occur in decreasing or non-veridical contexts.

N-words in OT

N-words mark ‘negative’ variables (Corblin and Tovena 2003).

Functional motivation: mark focus of negation (Haspelmath 1997).

In OT terms: faithfulness constraint MaxNeg.

MaxNeg: Mark an argument under negation as negative (use negative indefinites in the scope of an anti-additive operator).

Constraint interaction

Relevant Rankings (OT syntax)

FaithNeg >> *Neg >> MaxNeg

[produce indefinites]

FaithNeg >> MaxNeg >> *Neg

[produce n-words]

Indefinites (production)

Meaning x1x2

Form FNeg *Neg MaxNeg

indef+indef * **

neg+indef * *

neg+neg **

Dutch, German, Turkish,..

N-word (production)

Meaning x1x2

Form FNeg MaxNeg *Neg

indef+indef * **

neg+indef * *

neg+neg **

Romance, Slavic, Greek, Hungarian..

Interpretation

Issue: Does a sequence of neg items that express x in isolation express a single or a double (multiple) negation?

InterpretNeg (IntNeg): Interpret all neg expressions in the input as contributing a negative meaning in the output.

Ranking

MaxNeg and IntNeg are mirror images of each other (syntax/semantics).

Relevant rankings to consider for interpretation:

FaithNeg >> *Neg >> IntNeg [NC]

FaithNeg >> IntNeg >> *Neg [DN]

DN (interpretation)

Form neg+neg

Meaning FNeg IntNeg *Neg

x1x2 * **

x1x2 * *

x1x2 **

NC (Interpretation)

Form neg+neg

Meaning FNeg *Neg IntNeg

x1x2 * **

x1x2 * *

x1x2 **

Bi-directional grammar

Negative concord:

MaxNeg >> *Neg >> IntNeg

‘Mark negative variables’

Double negation:

IntNeg >> *Neg >> MaxNeg

‘First-order compositional meaning’

Results so far

Whether a neg expression is interpreted as a negative quantifier or as an n-word depends on bi-directional grammar, not on lexical meaning (uniformly ).

Constraints are universal, ranking is language-specific (NC vs. DN).

Reranking = typology in OT

Other rankings?

Three constraints allow 6 rankings:

MaxNeg >> *Neg >> IntNeg NC

MaxNeg >> IntNeg >> *Neg unstable

*Neg >> MaxNeg >> IntNeg unstable

*Neg >> IntNeg >> MaxNeg unstable

IntNeg >> MaxNeg >> *Neg unstable

IntNeg >> *Neg >> MaxNeg DN

Recoverability problem

meaning

form MaxNeg IntNeg *Neg

neg+indef * *

neg+neg **

form neg+neg

meaning

* **

**

Sentential negation

Haspelmath (1997): subtypes of negative indefinites, depending on relation to marker of negation.

o Class I: SN mandatory (Rumanian, Greek, Afrikaans, Polish,..) (strict NC)

o Class II: SN impossible (Dutch, English)o Class III: SN with postverbal n-words only

(Italian, Spanish, Portuguese). (non-strict NC)

Non-strict NC: asymmetry

Preverbal versus postverbal n-words, e.g. Spanish, Portuguese, Italian, ..

Maria non ha parlato con nessuno.

Maria sn has talked to nobody.

Nessuno ha parlato con nessuno.

*Maria ha parlato di niente con nessuno

*Nessuno non ha parlato con nessuno.

Non-strict NC in OT

NegFirst: Negation is preverbal (Horn)

Postverbal n-word with SN (Ladusaw 1992: clausal scope).

meaning Vx

form NegFirst MaxNeg *Neg

V neg * *

sn V neg **

Preverbal n-word

Relevant for production only!

meaning xV

form NegFirst MaxNeg *Neg IntNeg

neg V *

neg sn V **

Strict NC: mandatory SN

Negative indefinites always co-occur with SN: Rumanian, Greek, Polish,..

Nikt nie przyszekl [Polish]

Nobody SN came.

Nie widzialam nikogo.

SN saw nobody

Strict NC in OT

MaxSN: a negative clause must bear a marker of sentential negation (sn)

Relevant for production only!

Meaning x1Vx2

form MaxSN MaxNeg *Neg

neg V neg * **

neg sn V neg ***

Special Case: Catalan

En Pere no ha fet res.

The Peter SN has done nothing.

*En Pere ha fet res.

Ningú (no) ha vist en Joan.

Nobody (SN) has seen John.

Preverbal SN required for postverbal n-word, optional for preverbal n-word.

Postverbal n-word

NegFirst active: insertion of SN.

meaning form NegFirst MaxSN < >*Neg

Vx V neg * * *

sn V neg **

Pre-verbal n-word

MaxSN and *Neg equal in ranking.

Language change in progress: Spanish influence leads to demotion MaxSN.

meaning form NegFrst MaxSN< >*Neg

x1Vx2 neg V neg * **

neg sn V neg ***

Special case: French

Written French: type I language, preverbal ne always required.

Il ne vient pas. Il ne dit rien.

He SN comes SN. He SN says nothing.

Spoken French: demotion of MaxSN.

Il vient pas. Il dit rien. He comes SN He says nothing

Written French

Preverbal ànd postverbal n-words require ne: Il ne dit rien.

meaning form MaxSN *Neg

Vx V neg * *

ne V neg **

ne V pas neg ***

Spoken FrenchNeither preverbal nor postverbal n-word requires ne: Il dit rien.

Language change in progress: demotion of MaxSN.

meaning Vx

form *Neg MaxSN

V neg * *

ne V neg **

V pas neg ** *

Negative clauses

Written French: Il ne vient pas

Meaning P(a)

form FNeg MaxSN *Neg

NP ne V * *

NP V pas * * NP ne V pas **

Negative clauses

Spoken French: Il vient pas.

Meaning P(a)

form FaithNeg *Neg MaxSN

NP ne V * *

NP V pas * * NP ne V pas **

Double negation

DN in French: (ne..) pas + n-word.

Il n’est pas venu pour rien. He SN has not come for nothing. ‘He has not come for nothing.’ [DN]

Unexpected: combination pas + n-word does not come out as optimal form in tableaux so far.

Weak bi-directional optimality

Weak bi-directional optimality: ‘superoptimality’ (Blutner)

Unmarked forms-unmarked meanings; marked forms-marked meanings.

<f1,m1> <f1,m2> <f2,m1> <f2,m2>

DN in French

Input [f,m]

f1: neg; f2: pas+neg

m1: xp; m2: xp

*Neg IntNeg

[neg, xp] **

[neg, xp] ***

[pas+neg, xp] *** *

[pas+neg, xp] ****

DN in Afrikaans

Hy het nie haar verjaarsdag vergeet nie. He has sn her birthday forgotten sn ‘Her sister didn’t forget her birthday.’

Hulle het nooit gesing nie. They have never sung sn ‘They have never sung.’ [NC]

Hy kon nie niemand gesien het nie. He could sn nobody saw has sn ‘He could not have seen nobody’ [DN]

DN in Italian

Non-strict NC languages: block sentential negation with preverbal n-words.Marginal DN readings, e.g. Italian (Zanuttini 1991).Nessuno degli studenti non è venuto.

None of the students sn is come. ‘None of the students hasn’t come’ [DN]

DN in Welsh

Fuo’ fo *(ddim) yn gweithio erioed. be.past.3sg he SN prog work never. ‘He has never worked.’ [NC]

Dydy hi erioed ddim wedi helpu. neg.be3sg she never SN perf help ‘She has never not helped.’ [DN]

Lexicon or grammar?

Pas always incompatible with n-words, so lexical account de Swart & Sag OK.Afrikaans nie, Italian non and Welsh ddim not incompatible with n-words, but DN readings in certain configurations.OT analysis predicts DN readings in cases in which presence of SN is not required by OT syntax.

Conclusions of the day I

DN languages first-order compositional, NC languages require resumptive quantification, because they mark ‘negative variables’, .

Bi-directional OT grammar leads to typology of negation in terms of ranking of three constraints: MaxNeg, IntNeg and *Neg.

Conclusions of the day II

Marker of SN gets absorbed in resumptive polyadic quantifier, and plays no role in semantics of NC.Role of marker of SN: purely syntactic (scope marker: strict vs. non-strict NC).Weak bi-directional optimality: DN readings in configurations where SN is not required to express NC.